Reliability Modeling And Assessment For Multi-State Systems With State Transition Dependency

As engineered systems become more complex,sophisticated,intelligent,and large-scale,system reliability and safety become increasingly pressing.To ensure systems being reliably working,there is an urgent need to model the degradation trend of engineered systems and assess their reliability over time.On the one hand,engineered systems and components possess multiple states when deteriorating from a perfectly functioning state to a completely failed state.On the other hand,due to the hetergenousity of failure mechanisms,components' degradation behaviors are distinct.Hence,it is a challenge to analyze reliability of systems suffering from degradation.Additionally,as components located adjacently suffer from the same working/ environmental conditions and/or interact with one another,some components in a system may be stochastically dependent and the time durations of a component sojourning at some particular states are not stochastically independent.This dissertation devotes to modeling the state transition dependency of multi-state systems,inferring the unknown model parameters by observation data,and assessing system reliability.The primary research contributions and innovative outcomes are summarized as follows:(1)Development of a reliability assessment method for multi-state systems with state transition dependency.By considering the dependency among state transitions of a multi-state system,a new multi-state system reliability model is proposed.The dependency among state transitions is implicitly characterized by copula functions,and the likelihood functions for model parameter estimation are formulated for two cases,i.e.,continuous and discontinuous inspection strategies.The existing model selection criterias are customized to identify the preferable model among candidates,and the reliability function of a population of multi-state systems and the conditional reliability function of each individual multi-state system given a set of observations are derived.Two illustrative examples show that the state transition dependency can produce a nonignorable discrepancy in the assessment of state distribution and reliability function of MSSs as compared to the independent case.(2)Development of a reliability evaluation method for partially observed multi-state systems with state transition dependency.By taking account of partial observations,a new reliability model for multi-state systems with state transition dependency is put forth.The dependency between state transitions is characterized by copula functions,whereas the uncertainty associated with partial observations is quantified by an observation probability matrix.The unknown parameters in the new multi-state system model are inferred by a tailored Expectation Maximization(EM)algorithm,while the reliability function of a population of multi-state systems and the conditional reliability for a specific invidiual system are derived.Two illustrative examples,together with a set of comparative studies,are presented to examine the performance of the proposed method.(3)Development of a reliability assessment method for systems with two types of degradation components.By taking account of hetergenous degradation behaviors of components in a system,multi-state models and stochastic process models are used jointly to characterize the degradation of a system.The dependency among state transitions of a multi-state component is implicitly characterized by copula functions.By considering the dependency between a multi-state component and a component subject to continuous degradation,a multi-stage stochastic Gamma degradation process model is developed to assess the system reliability.The likelihood functions for model parameter estimation are formulated for two cases,i.e.,synchronous and asynchronous inspection strategies.The Monte Carlo simulation algorithm is used to compute the system reliability.The results from the illustrative examples show that,as compared to the independent cases,the state transition dependency within a multi-state component and the degradation dependency between components can produce significant impact on the result of system reliability assessment.